Drawing graphs

Our data

To illustrate making graphs, we need some data.
Data on 202 male and female athletes at the Australian Institute of Sport.
Variables:
- categorical: Sex of athlete, sport they play
- quantitative: height (cm), weight (kg), lean body mass, red and white blood cell counts, haematocrit and haemoglobin (blood), ferritin concentration, body mass index, percent body fat.
Values separated by tabs (which impacts reading in).

Packages for this section

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library(tidyverse)

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library(tidyverse)

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Reading data into R

Use read_tsv (“tab-separated values”), like read_csv.
Data in ais.txt:

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my_url <- "http://ritsokiguess.site/datafiles/ais.txt"
athletes <- read_tsv(my_url)

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my_url <- "http://ritsokiguess.site/datafiles/ais.txt"
athletes <- read_tsv(my_url)

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The data (some)

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athletes

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athletes

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Types of graph

Depends on number and type of variables:

Categorical	Quantitative	Graph
1	0	bar chart
0	1	histogram
2	0	grouped bar charts
1	1	side-by-side boxplots
0	2	scatterplot
2	1	grouped boxplots
1	2	scatterplot with points identified by group (eg. by colour)

With more (categorical) variables, might want separate plots by groups. This is called facetting in R.

`ggplot`

R has a standard graphing procedure ggplot, that we use for all our graphs.
Use in different ways to get precise graph we want.
Let’s start with bar chart of the sports played by the athletes.

Bar chart

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ggplot(athletes, aes(x = Sport)) + geom_bar()

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ggplot(athletes, aes(x = Sport)) + geom_bar()

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Histogram of body mass index

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ggplot(athletes, aes(x = BMI)) + geom_histogram(bins = 10)

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ggplot(athletes, aes(x = BMI)) + geom_histogram(bins = 10)

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Which sports are played by males and females?

Grouped bar chart:

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ggplot(athletes, aes(x = Sport, fill = Sex)) +
  geom_bar(position = "dodge")

BMI by gender

ggplot(athletes, aes(x = Sex, y = BMI)) + geom_boxplot()

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ggplot(athletes, aes(x = Sport, fill = Sex)) +
  geom_bar(position = "dodge")

BMI by gender

ggplot(athletes, aes(x = Sex, y = BMI)) + geom_boxplot()

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Height vs. weight

Scatterplot:

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ggplot(athletes, aes(x = Ht, y = Wt)) + geom_point()

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ggplot(athletes, aes(x = Ht, y = Wt)) + geom_point()

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With regression line

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ggplot(athletes, aes(x = Ht, y = Wt)) +
  geom_point() + geom_smooth(method = "lm")

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ggplot(athletes, aes(x = Ht, y = Wt)) +
  geom_point() + geom_smooth(method = "lm")

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BMI by sport and gender

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ggplot(athletes, aes(x = Sport, y = BMI, fill = Sex)) +
  geom_boxplot()

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ggplot(athletes, aes(x = Sport, y = BMI, fill = Sex)) +
  geom_boxplot()

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A variation that uses colour instead of fill:

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ggplot(athletes, aes(x = Sport, y = BMI, colour = Sex)) +
  geom_boxplot()

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ggplot(athletes, aes(x = Sport, y = BMI, colour = Sex)) +
  geom_boxplot()

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Height and weight by gender

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ggplot(athletes, aes(x = Ht, y = Wt, colour = Sex)) +
  geom_point()

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ggplot(athletes, aes(x = Ht, y = Wt, colour = Sex)) +
  geom_point()

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Filling each facet

Default uses same scale for each facet. To use different scales for each facet, this:

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ggplot(athletes, aes(x = Ht, y = Wt, colour = Sex)) +
  geom_point() + facet_wrap(~Sport, scales = "free")

Another view of height vs weight

ggplot(athletes, aes(x = Ht, y = Wt)) +
  geom_point() + facet_wrap(~ Sex)

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ggplot(athletes, aes(x = Ht, y = Wt, colour = Sex)) +
  geom_point() + facet_wrap(~Sport, scales = "free")

Another view of height vs weight

ggplot(athletes, aes(x = Ht, y = Wt)) +
  geom_point() + facet_wrap(~ Sex)

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Normal quantile plot

For assessing whether a column has a normal distribution or not:

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ggplot(athletes, aes(sample = BMI)) + stat_qq() + stat_qq_line()

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ggplot(athletes, aes(sample = BMI)) + stat_qq() + stat_qq_line()

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Comments

Data on \(y\)-axis
on \(x\)-axis, the \(z\)-scores you would expect if normal distribution correct
if the points follow the line, distribution is normal
the way in which the points don’t follow line tell you about how the distribution is not normal
in this case, the highest values are too high (long upper tail).

Facetting

Male and female athletes’ BMI separately:

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ggplot(athletes, aes(sample = BMI)) + stat_qq() + stat_qq_line() +
  facet_wrap(~ Sex)

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ggplot(athletes, aes(sample = BMI)) + stat_qq() + stat_qq_line() +
  facet_wrap(~ Sex)

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Comments

The distribution of BMI for females is closer to normal, with only the highest few values being too high
The distribution of BMI values for males might even be right-skewed: not only are the upper values too high, but some of the lowest ones are not low enough.

More normal quantile plots

How straight does a normal quantile plot have to be?
There is randomness in real data, so even a normal quantile plot from normal data won’t look perfectly straight.
With a small sample, can look not very straight even from normal data.
Looking for systematic departure from a straight line; random wiggles ought not to concern us.
Look at some examples where we know the answer, so that we can see what to expect.

Normal data, large sample

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d <- tibble(x=rnorm(200))
ggplot(d, aes(x=x)) + geom_histogram(bins=10)

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d <- tibble(x=rnorm(200))
ggplot(d, aes(x=x)) + geom_histogram(bins=10)

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The normal quantile plot

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ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

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ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

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Normal data, small sample

Not so convincingly normal, but not obviously skewed:

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d <- tibble(x=rnorm(20))
ggplot(d, aes(x=x)) + geom_histogram(bins=5)

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d <- tibble(x=rnorm(20))
ggplot(d, aes(x=x)) + geom_histogram(bins=5)

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The normal quantile plot

Good, apart from the highest and lowest points being slightly off. I’d call this good:

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ggplot(d, aes(sample=x)) + stat_qq() + stat_qq_line()

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ggplot(d, aes(sample=x)) + stat_qq() + stat_qq_line()

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Chi-squared data, df = 10

Somewhat skewed to right:

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d <- tibble(x=rchisq(100, 10))
ggplot(d,aes(x=x)) + geom_histogram(bins=10)

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d <- tibble(x=rchisq(100, 10))
ggplot(d,aes(x=x)) + geom_histogram(bins=10)

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The normal quantile plot

Somewhat opening-up curve:

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ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

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ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

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Chi-squared data, df = 3

Definitely skewed to right:

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d <- tibble(x=rchisq(100, 3))
ggplot(d, aes(x=x)) + geom_histogram(bins=10)

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d <- tibble(x=rchisq(100, 3))
ggplot(d, aes(x=x)) + geom_histogram(bins=10)

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The normal quantile plot

Clear upward-opening curve:

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ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

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ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

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t-distributed data, df = 3

Long tails (or a very sharp peak):

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d <- tibble(x=rt(300, 3))
ggplot(d, aes(x=x)) + geom_histogram(bins=15)

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d <- tibble(x=rt(300, 3))
ggplot(d, aes(x=x)) + geom_histogram(bins=15)

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The normal quantile plot

Low values too low and high values too high for normal.

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ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

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ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

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Summary

On a normal quantile plot:

points following line (with some small wiggles): normal.
kind of deviation from a straight line indicates kind of nonnormality:
- a few highest point(s) too high and/or lowest too low: outliers
- else see how points at each end off the line:

	High points
Low points	Too low	Too high
Too low	Skewed left	Long tails
Too high	Short tails	Skewed right

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Drawing graphs

Our data

Packages for this section

Reading data into R

The data (some)

Types of graph

`ggplot`

Bar chart

Histogram of body mass index

Which sports are played by males and females?

BMI by gender

BMI by gender

Height vs. weight

With regression line

BMI by sport and gender

Height and weight by gender

Height by weight by gender for each sport, with facets

Height by weight by gender for each sport, with facets

Filling each facet

Another view of height vs weight

Another view of height vs weight

Normal quantile plot

Comments

Facetting

Comments

More normal quantile plots

Normal data, large sample

The normal quantile plot

Normal data, small sample

The normal quantile plot

Chi-squared data, df = 10

The normal quantile plot

Chi-squared data, df = 3

The normal quantile plot

t-distributed data, df = 3

The normal quantile plot

Summary